Light incident normally on a plane mirror attached to a galvanome… - Vidyadip

Question

Light incident normally on a plane mirror attached to a galvanometer coil retrace backwards (as shown in Fig.). A current in the coil produces a deflection of 3.5° of the mirror. What is the displacement of the reflected spot of light on a screen placed 1.5 m away?

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Answer

Here we know that the reflected rays are deflected at an angle twice to the angle of rotation of the mirror. From the figure we see that when the mirror is turned from M to M'position by an angle theta = 3.5 deg The reflected ray OB is bent as:

$\angle 2 \theta=2 \times 3.5^{\circ}=7^{\circ}=\angle AOB$.
In right triangle $AOB , \tan 2 \theta=\frac{ AB }{ AO }$
or $\tan 7^{\circ}=\frac{d}{1.5}$
$\begin{aligned} d & =1.5 \times \tan 7^{\circ} \\ & =1.5 \times 0.1228 \\ & =0.1842 m \\ & =18.42 cm .\end{aligned}$

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